Chlorination is by far the most common method of wastewater disinfection and is used worldwide for the disinfection of pathogens before discharge into receiving streams, rivers or oceans. Chlorine is known to be effective in destroying a variety of bacteria, viruses and protozoa, including Salmonella, Shigella and Vibrio cholera. 
Wastewater chlorination was initially applied in the early 1900 s and was soon implemented in many other cities in the United States based on this early success. Today, wastewater chlorination is widely practiced to reduce microbial contamination and potential disease risks to exposed populations.
There is a water use cycle in which drinking water is treated, then consumed and discharged as wastewater. Following additional treatment, wastewater is discharged and may enter source waters used for drinking and recreation. The treatment-use-discharge process then begins again, continuing the water use cycle.
A typical wastewater chlorination reactor 100 is shown in FIG. 1, where the process of chlorination is carried out in a reactor of rectangular cross section and rectangular profile. Water enters the basin at an inlet flow rate Q(t) in cubic meters per second (m3/s), where the variable t denotes time (in seconds), and is treated with a dose of chlorine injected through a chlorine-rich stream Qd(t). The injected chlorine mixes with the water in the entrance region of the reactor denoted as dosage basin 15 in FIG. 1, where the water quickly adopts a chlorine concentration C0(t) that is measured by a concentration transducer (CT) 8 that produces an on-line measurement of chlorine concentration. The water then enters the ensuing section of the reactor, denoted as contact basin 18 in FIG. 1, where the chlorine effects further disinfection. The demarcation between the dosage basin 15 and the contact basin 18, shown by the vertical dash-dot line 12 in FIG. 1, which may be physically defined by the presence of baffles or other agitation, equipment, or be implicitly defined by the location of the concentration transducer 8.
FIG. 1 is not drawn to scale, and contact basin 18 is typically much larger than the dosage basin 15. The contact basin 18 has a length L (m), and the coordinate z is used to characterize specific locations along the horizontal direction, with z=0 (m) denoting the beginning of the contact basin and z=L (m) denoting the location where the water exits the contact basin 18. The width of the basin is denoted by W(m) (not shown in FIG. 1). The outlet of the contact basin 18 includes a weir 11 over which the water flows out of the basin at a flow rate Qw(t). The weir 11 shown in FIG. 1 is static, which means that its height, denoted by hw in FIG. 1, is set to a fixed value and is not intended to be further adjusted during normal operation. The height of water in the basins, denoted by h in FIG. 1, is normally not very deep, with typical values ranging from 1 to 3 m, which remain approximately constant at all locations z along the contact basin 18.
The wastewater chlorination process typically makes use of a master controller (MC) 9, along with a ratio controller (RC) 6. Some wastewater treatment plants use an additional slave controller (SC) 7 as shown in FIG. 1 arranged in cascade with MC 9 to further improve performance. The control configuration of FIG. 1 is known as a cascade/ratio control scheme for chlorine dosage adjustment. The MC 9 and SC 7 controllers are most commonly of the proportional-integral-derivative (PID) type. The cascade configuration of controllers, ratio control, and PID control are mature technologies that are well known to those with ordinary skill in the art.
The cascade/ratio control architecture for chlorine dosage adjustment shown in FIG. 1 first uses controller SC 7 to compare the chlorine concentration measurement C0(t) produced by CT 8 with the set-point Coo(t) which represents the target value of chlorine concentration desired at location z=0, and produces a prescribed value of the ratio of the dosage flow rate to the inlet flow rate, namely R(t). Ratio controller 6 makes use of the prescribed value of the ratio R(t) produced by SC 7 along with the value of the inlet flow rate Q(t) measured by the flow transducer FT 4 to produce the prescribed value of the dosage stream Qd(t). The plant operator generally specifies the set-point. However, the specification is made automatically by the MC 9 when a cascade configuration is implemented. MC 9 produces the required specification after comparing the outlet chlorine concentration CL(t) measured by the concentration transducer (CT) 10, with the operator-specified the set-point CLo(t), which is the desired value of chlorine concentration in the outlet stream. The controllers SC 7, MC 9, and RC 6 feature adjustable parameters, such as gains and integral time-constants, that must be adjusted using standard parameter-tuning techniques that are well known to those with ordinary skill in the art. The cascade system with ratio control is expected to ensure that the treated water satisfies environmental regulations often imposed by the government, such as the chlorine concentration CL(t) in the outlet flow being greater than 1 ppm, and that the residence τres(t) time,                                           τ            res                    ⁡                      (            t            )                          =                  L          ⁢                                          ⁢          W          ⁢                                    h              ⁡                              (                t                )                                                    Q              ⁡                              (                t                )                                                                        (        1        )            being greater than 15 min.
A numerical simulation study was used to characterize the performance of the conventional wastewater processing system and associated control scheme shown in FIG. 1. The one-dimensional (z-direction) chlorine concentration profile in the contact basin can be described by the reaction-diffusion equation:                                           ∂            C                                ∂            t                          =                                            -                              v                ⁡                                  (                  t                  )                                                      ⁢                                          ∂                C                                            ∂                z                                              +                      r            C                    +                      D            ⁢                                                            ∂                  2                                ⁢                C                                            ∂                                  z                  2                                                                                        (        2        )            and by the conservation of mass equation:                                           ⅆ                          h              ⁡                              (                t                )                                                          ⅆ            t                          =                                            1              LW                        ⁢                          Q              ⁡                              (                t                )                                              -                                    1              LW                        ⁢                                          Q                w                            ⁡                              (                t                )                                                                        (        3        )            where C denotes the concentration of chlorine at a location z and at a time instant t, the variable rc denotes the rate of consumption of chlorine by chemical reaction and by volatilization, D denotes the dispersion coefficient for chlorine in water, and v(t)=Q(t)/(Wh(t)) is the linear velocity of the water in the basin. It is assumed that controllers SC and RC are highly effective and therefore they ensure attainment of the boundary condition C(t, z)=Coo(t) at z=0.
The solution of the partial differential equation (2) is accomplished via standard numerical methods, including a method that approximates (2) using a finite number of ordinary differential equations, obviating the need for identifying the value of the dispersion coefficient. The rate of chlorine consumption via chemical reaction and volatilization was modeled as rc=−kC, where k=0.000109 s−1 based on data from a representative experimental wastewater treatment plant. The outlet flow rate Qw(t) was modeled using the well-known Francis weir equation. Finally, the controllers SC 7 and MC 9 were of the PID form, tuned by an exhaustive trial-and-error procedure, with the set point to MC 9 fixed at Coo(t)=2 ppm. The total basin length was 120 m, and the width was W=8 m. More specifically, the length of the contact basin 18 was L=117.6 m, with the length of the dosage basin 15 making up the remainder of the total length. Without loss of generality, throughout the simulation study it is assumed that the weir was deployed with no suppressions, meaning that the width of the basin W is equal to the width of the weir ww.
Typical results from a computer simulation of system 100 performed using the cascade/ratio configuration shown in FIG. 1 is presented in FIG. 2, where FIG. 2(a) shows that the inlet flow rate Q(t) as a sine wave that varies in amplitude from 0.1 m3/s to 0.7 m3/s over a one-day period corresponding to a seven-fold fold change between the maximum and minimum inlet flow rates. Such sinusoidal profiles are representative of the cycle of water usage in a typical community throughout a day. FIG. 2(d) shows that, in spite of the best effort of the cascade/ratio control system, the outlet-water chlorine concentration CL(t) oscillates between its smallest value of 0.5 ppm where it violates conventional regulations which require a minimum of 1 ppm of chlorine and its largest value of 6.9 ppm where the unnecessarily high concentration represents a costly waste of chlorine. FIG. 2(c) shows the inlet dose-concentration Co(t) while FIG. 2(b) shows residence time τres(t) realized by the cascade/ratio control system 100 for chlorine dosage adjustment. As shown in FIG. 2(b), the large fluctuations of the inlet flow rate cause a highly variable residence time. The residence time oscillates between a minimum value of 35 min to a maximum value of 231 min. Hence, when the flow rates are low the water resides in the basin for a relatively long time, and consequently a very large amount of chlorine is lost via chemical reaction and volatilization leading to a violation of regulations requiring minimal outflow concentration levels. On the other hand, when the inlet flow rate is high the ensuing short residence time does not give the reaction and volatilization processes time to proceed to a significant extent, and consequently the water exits the contact basin with undesirably high chlorine concentrations. Therefore, the outlet chlorine concentration set point cannot simply be increased to avoid violation, as the accompanying over-chlorination problem would be exacerbated.
This simulation results shown in FIGS. 2(a)–(d) illustrate the limitations of a system 100 which utilizes a conventional cascade/ratio control configuration. A major problem with such a system is that the large fluctuations in input flow rate cause undesirable fluctuations in residence time, and a concomitant degradation of concentration-control performance which results because none of the controllers in the cascade/ratio configurations of FIG. 1 are designed to keep the residence time from experiencing such strong variations.